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3 years ago

What is the volume of the given prism? round the answer to the nearest tenth. please explain :(

Mathematics

2 answers:

sveticcg [70]3 years ago

4 0

The equation to finding the area of a triangular prism is 1/4*height $\sqrt{x}$ -a^4 + 2 * (a*b)^2 + 2(a*c) - b^4 + 2(b*c)^2 - c^4. (I know that's really confusing)

The A, B, and C values all stand for the base side lengths of the 2 triangles. The h is height. Plug in these values to the equation, and your answer is 3436.4 yards cubed. I hope this helped.

My name is Ann [436]3 years ago

4 0

Answer:

Option C. 6872.8 yd³

Step-by-step explanation:

Since volume of the triangular prism = Area of square base × height of prism

Area of square base = length × width = 16×31 = 496 yd²

Height of the prism (By Pythagoras theorem) = Height of the isosceles triangle = $\sqrt{(16^{2}-8^{2})}= \sqrt{256-64}$

= $\sqrt{192}$

= $8\sqrt{3}$ yd

Now we put these values in the formula of volume

Volume = 496×8√3 = 496×(13.86) = 6872.8 yd³

Answer is option C. 6872.8 yd³

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A regulation baseball has a diameter of about 3 in.

Elena L [17]

ANSWER: I think that the answer is 28.26

Step-by-step explanation:

I did this a while ago. I hope that I helped<3

3 0

2 years ago

(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.

valentinak56 [21]

Find the intersection of the two planes. Do this by solving for z in terms of x and y ; then solve for y in terms of x ; then again for z but only in terms of x.

-4x + 2y - z = 1 ==> z = -4x + 2y - 1

3x - 2y + 2z = 1 ==> z = (1 - 3x + 2y)/2

==> -4x + 2y - 1 = (1 - 3x + 2y)/2

==> -8x + 4y - 2 = 1 - 3x + 2y

==> -5x + 2y = 3

==> y = (3 + 5x)/2

==> z = -4x + 2 (3 + 5x)/2 - 1 = x + 2

So if we take x = t, the line of intersection is parameterized by

r(t) = ⟨t, (3 + 5t )/2, 2 + t⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

(a) The tangent vector to r(t) is parallel to this line, so you can use

v = dr/dt = d/dt ⟨2t, 3 + 5t, 4 + 2t⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in x = -1, y = 1, and z = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

r(t) = ⟨2t, 3 + 5t, 4 + 2t⟩

3 0

2 years ago

Log(x+6)-log(x-3)=1 I need to show work, please show me how

Illusion [34]

Answer:

x = 4.

Step-by-step explanation:

log(x + 6)- log(x - 3) = 1

Using the law log a - log b = log a/b:

log (x + 6)/ (x - 3) = 1

Removing logs:

(x + 6)/ (x - 3) = 10

x+ 6 = 10x - 30

9x = 36

x = 4 (answer).

8 0

3 years ago

Read 2 more answers

Test for the commutative property of union and intersection of the sets P = { x : x is all real numbers between 2 and 7} and Q =

In-s [12.5K]

Answer:

Step-by-step explanation:

P = {x : x is a real number between 2 and 7}

{x: 3,4,5,6}

Q = {x : x is all rational number between 2 and 7}

{4 }

We know that P contains all the rational numbers between 2 and 7.

And P ∪ Q and Q ∪ P each of them contain all the real numbers which are between 2 and 7.

{3,4,5,6}

Here Q is the proper subset of P

P ∩ Q = Q ∩ P = Q= {4}

4 0

3 years ago

The sum of 3 consecutive number multiples of 6 is 162 find thesse numbers

MAXImum [283]

let the numbers are x , x+1 ,x+2

∴ 6 [ x + (x+1) +(x+2) ] = 162

∴ x + (x+1) + (x+2) = 162/6 = 27

∴3x + 3 = 27

∴ 3x = 27 - 3 = 24

∴ x = 24/3 = 8

So, the numbers are 8 , 9 , 10

7 0

3 years ago